FIA NLS Models: Biomass vs. Stand Age (Temporally-Balanced dataset) – with Biomass Partitioning for the Eastern US
JAH
2023-07-12
Background
This analysis document compliments FIA NLS Models: Biomass vs. Stand Age. All of the background information from that document applies to these analyses, which are extensions to them. In this analysis, we fit models to the temporally-balanced dataset, which uses the first and most-recent plot re-measurement for each FIA plot. Then, we conduct a model bookeeping analysis, which does biomass change attribution to:
- age-related biomass change
- productivity-trend driven biomass change
- disturbance regime (changes in the biomass loss rate)- attributable biomass change
Below the model fitting procedure is implemented by ecoprovince:
Using temporally-balanced data
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4834 1203.6
## 2 4833 1092.6 1 111.05 491.22 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 52557.62
## 2 2 52091.41##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.45951 0.16992 2.704 0.00687 **
## alpha 0.84855 0.03503 24.221 < 2e-16 ***
## A 473.76484 37.00356 12.803 < 2e-16 ***
## k 205.69316 18.21698 11.291 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4755 on 4833 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.017e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) :
## object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) :
## object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) :
## object 'Mod.Sel3' not found
## model AIC
## 1 2 52091.41
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.45951 0.16992 2.704 0.00687 **
## alpha 0.84855 0.03503 24.221 < 2e-16 ***
## A 473.76484 37.00356 12.803 < 2e-16 ***
## k 205.69316 18.21698 11.291 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4755 on 4833 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.017e-06
## (1 observation deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4832 1179.6
## 2 4831 1067.7 1 111.87 506.17 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 52091.41
## 2 4 52463.90
## 3 5 51983.93##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.58118 0.17752 3.274 0.00107 **
## alpha 0.84078 0.03411 24.646 < 2e-16 ***
## a 33.40070 1.99286 16.760 < 2e-16 ***
## b 118.88478 5.92661 20.059 < 2e-16 ***
## c 118.37512 5.85956 20.202 < 2e-16 ***
## d 1.01653 0.05233 19.425 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4701 on 4831 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12943 5165.4
## 2 12942 5044.1 1 121.33 311.3 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 135621.4
## 2 2 135315.7##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.95237 0.12759 7.464 8.91e-14 ***
## alpha 0.62169 0.03318 18.736 < 2e-16 ***
## A 165.96924 5.63575 29.449 < 2e-16 ***
## k 78.87707 3.15407 25.008 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6243 on 12942 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 8.623e-06
## (16 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12942 5044.1
## 2 12941 5021.8 1 22.266 57.378 3.839e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 135315.7
## 2 2a 135260.4
## 3 2b 135317.6
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 9.238e-01 1.259e-01 7.336 2.33e-13 ***
## alpha 6.214e-01 3.094e-02 20.082 < 2e-16 ***
## A 1.921e+02 9.346e+00 20.559 < 2e-16 ***
## k 1.085e+02 7.979e+00 13.593 < 2e-16 ***
## p 2.121e-02 2.492e-03 8.509 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6229 on 12941 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 5.063e-06
## (16 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12941 5088.9
## 2 12940 4912.4 1 176.51 464.95 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 135260.4
## 2 4 135432.3
## 3 5 134977.3##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.19051 0.13607 8.749 <2e-16 ***
## alpha 0.67333 0.02702 24.922 <2e-16 ***
## a 13.38590 0.51341 26.073 <2e-16 ***
## b 75.80154 2.36631 32.034 <2e-16 ***
## c 121.05709 5.45544 22.190 <2e-16 ***
## d 1.41595 0.04287 33.030 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6161 on 12940 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (16 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5442 948.80
## 2 5441 857.87 1 90.926 576.69 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 59550.63
## 2 2 59004.09##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.1644 0.1261 1.304 0.192
## alpha 0.8050 0.0312 25.799 <2e-16 ***
## A 500.5614 30.8115 16.246 <2e-16 ***
## k 155.6108 11.1725 13.928 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3971 on 5441 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.272e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5441 857.87
## 2 5440 856.53 1 1.3429 8.529 0.00351 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 59004.09
## 2 2a 58997.56
## 3 2b 58973.93
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.23383 0.13009 1.797 0.0723 .
## alpha 0.81624 0.03142 25.975 <2e-16 ***
## A 293.53650 21.44552 13.688 <2e-16 ***
## k 64.20469 6.41740 10.005 <2e-16 ***
## s 1.31952 0.05962 22.132 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3959 on 5440 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.275e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5440 940.37
## 2 5439 848.31 1 92.062 590.26 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 58973.93
## 2 4 59506.03
## 3 5 58947.03##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.24222 0.13018 1.861 0.0629 .
## alpha 0.80822 0.03087 26.178 < 2e-16 ***
## a 21.08256 2.67854 7.871 4.22e-15 ***
## b 179.51639 10.45102 17.177 < 2e-16 ***
## c 156.83930 15.71326 9.981 < 2e-16 ***
## d 1.51879 0.08979 16.915 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3949 on 5439 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3547 1178.6
## 2 3546 1136.5 1 42.068 131.25 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 38157.03
## 2 2 38030.00##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.03509 0.24350 4.251 2.18e-05 ***
## alpha 0.72686 0.05912 12.295 < 2e-16 ***
## A 445.56009 55.43529 8.037 1.24e-15 ***
## k 254.71684 34.82136 7.315 3.17e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5661 on 3546 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.413e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3546 1136.5
## 2 3545 1132.9 1 3.5914 11.238 0.00081 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 38030.00
## 2 2a 38020.77
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.091545 0.248065 4.400 1.11e-05 ***
## alpha 0.753308 0.059393 12.683 < 2e-16 ***
## A 342.271688 43.589966 7.852 5.38e-15 ***
## k 170.045425 28.883552 5.887 4.29e-09 ***
## p -0.015140 0.006514 -2.324 0.0202 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5653 on 3545 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 5.957e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3545 1160.1
## 2 3544 1108.8 1 51.282 163.91 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 38020.77
## 2 4 38104.80
## 3 5 37946.29##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.21145 0.25520 4.747 2.14e-06 ***
## alpha 0.76881 0.05439 14.134 < 2e-16 ***
## a 14.01898 1.39169 10.073 < 2e-16 ***
## b 101.92211 6.02465 16.918 < 2e-16 ***
## c 115.56990 8.21593 14.067 < 2e-16 ***
## d 1.19701 0.06667 17.955 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5593 on 3544 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6383 1208.6
## 2 6382 1143.1 1 65.521 365.81 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 66739.63
## 2 2 66385.70##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.80821 0.12030 6.718 2e-11 ***
## alpha 0.70093 0.03432 20.426 <2e-16 ***
## A 212.97304 8.46135 25.170 <2e-16 ***
## k 72.75583 3.94421 18.446 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4232 on 6382 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 2.25e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6382 1143.1
## 2 6381 1142.5 1 0.6350 3.5469 0.0597 .
## 3 6381 1136.2 0 0.0000
## 4 6380 1128.1 1 8.1539 46.1159 1.215e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 66385.70
## 2 2a 66384.15
## 3 2b 66349.16
## 4 2c 66305.16##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.85759 0.12173 7.045 2.05e-12 ***
## alpha 0.71209 0.03381 21.062 < 2e-16 ***
## A 127.11413 4.61707 27.531 < 2e-16 ***
## k 37.02397 1.25609 29.475 < 2e-16 ***
## p 0.14094 0.01883 7.486 8.09e-14 ***
## s 2.17271 0.15279 14.220 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4205 on 6380 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.063e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6381 1195.9
## 2 6380 1127.7 1 68.139 385.5 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 66305.16
## 2 4 66675.81
## 3 5 66303.16##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.84613 0.12109 6.988 3.08e-12 ***
## alpha 0.71122 0.03383 21.023 < 2e-16 ***
## a 17.80094 2.07031 8.598 < 2e-16 ***
## b 98.51432 3.90582 25.222 < 2e-16 ***
## c 113.18502 6.98395 16.206 < 2e-16 ***
## d 1.44570 0.07453 19.398 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4204 on 6380 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7773 2698.5
## 2 7772 2568.4 1 130.03 393.48 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 85845.56
## 2 2 85463.52##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.24476 0.17019 7.314 2.86e-13 ***
## alpha 0.57095 0.02662 21.444 < 2e-16 ***
## A 257.12975 11.27279 22.810 < 2e-16 ***
## k 67.16853 3.01370 22.288 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5749 on 7772 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.572e-06
## (14 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7772 2568.4
## 2 7771 2545.5 1 22.931 70.004 < 2.2e-16 ***
## 3 7771 2566.4 0 0.000
## 4 7770 2496.6 1 69.841 217.364 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 85463.52
## 2 2a 85395.79
## 3 2b 85459.40
## 4 2c 85246.85##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.506e+00 1.836e-01 8.201 2.76e-16 ***
## alpha 6.512e-01 2.258e-02 28.840 < 2e-16 ***
## A 1.450e+02 6.248e+00 23.205 < 2e-16 ***
## k 3.016e+01 1.222e+00 24.686 < 2e-16 ***
## p 1.076e-01 7.674e-03 14.024 < 2e-16 ***
## s 1.963e+00 9.744e-02 20.143 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5668 on 7770 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 5.033e-06
## (14 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7771 2669.8
## 2 7770 2494.5 1 175.36 546.22 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 85246.85
## 2 4 85766.57
## 3 5 85240.29##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.47599 0.18195 8.112 5.75e-16 ***
## alpha 0.65085 0.02255 28.860 < 2e-16 ***
## a 16.12785 0.82771 19.485 < 2e-16 ***
## b 120.36292 5.58045 21.569 < 2e-16 ***
## c 112.83900 9.26790 12.175 < 2e-16 ***
## d 1.63350 0.06625 24.657 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5666 on 7770 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (14 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7905 4072.2
## 2 7904 3928.6 1 143.61 288.94 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 88878.43
## 2 2 88596.51##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.76811 0.18004 4.266 2.01e-05 ***
## alpha 0.55314 0.02987 18.521 < 2e-16 ***
## A 270.07655 14.26944 18.927 < 2e-16 ***
## k 71.69928 3.93397 18.226 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.705 on 7904 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.137e-06
## (32 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7904 3928.6
## 2 7903 3859.0 1 69.597 142.53 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 88596.51
## 2 2a 88457.16
## 3 2b 88567.74
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 9.272e-01 1.885e-01 4.920 8.85e-07 ***
## alpha 6.432e-01 2.456e-02 26.191 < 2e-16 ***
## A 4.083e+02 4.091e+01 9.981 < 2e-16 ***
## k 1.596e+02 2.131e+01 7.489 7.67e-14 ***
## p 2.506e-02 1.901e-03 13.185 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6988 on 7903 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.089e-06
## (32 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7903 4029.5
## 2 7902 3773.8 1 255.69 535.39 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 88457.16
## 2 4 88799.14
## 3 5 88282.71##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.00852 0.19081 5.285 1.29e-07 ***
## alpha 0.71043 0.02138 33.233 < 2e-16 ***
## a 20.51866 1.02371 20.043 < 2e-16 ***
## b 121.27486 6.30094 19.247 < 2e-16 ***
## c 111.11452 9.25971 12.000 < 2e-16 ***
## d 1.50283 0.06832 21.998 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6911 on 7902 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (32 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 826 218.04
## 2 825 194.59 1 23.448 99.412 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9094.121
## 2 2 9001.802##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 3.865e-01 4.112e-01 0.940 0.3476
## alpha 7.628e-01 6.984e-02 10.922 <2e-16 ***
## A 1.255e+03 5.318e+02 2.360 0.0185 *
## k 4.893e+02 2.232e+02 2.192 0.0286 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4857 on 825 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.631e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_234, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 825 194.59
## 2 823 192.48 2 2.1059 4.5022 0.01136 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 9001.802
## 2 2a NA
## 3 2b NA
## 4 2c 8996.781##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.39536 0.41113 0.962 0.337
## alpha 0.78925 0.07021 11.242 < 2e-16 ***
## A 395.47217 189.29921 2.089 0.037 *
## k 99.96670 70.69953 1.414 0.158
## p -0.01220 0.01423 -0.857 0.392
## s 1.13109 0.24438 4.628 4.28e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4836 on 823 degrees of freedom
##
## Number of iterations to convergence: 40
## Achieved convergence tolerance: 3.1e-06
## (1 observation deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 824 216.69
## 2 823 192.29 1 24.399 104.43 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 8996.781
## 2 4 9092.966
## 3 5 8995.935##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4024 0.4120 0.977 0.32908
## alpha 0.7883 0.0701 11.246 < 2e-16 ***
## a 0.0000 5.9324 0.000 1.00000
## b 340.8238 204.3728 1.668 0.09576 .
## c 675.4071 940.5067 0.718 0.47288
## d 2.5547 0.6884 3.711 0.00022 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4834 on 823 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1387 347.56
## 2 1386 336.63 1 10.934 45.02 2.834e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 14526.30
## 2 2 14483.87##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.28977 0.25193 1.150 0.25
## alpha 0.68210 0.09544 7.147 1.43e-12 ***
## A 261.45525 28.66195 9.122 < 2e-16 ***
## k 106.87482 14.79744 7.223 8.39e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4928 on 1386 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 9.101e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1386 336.63
## 2 1385 336.63 1 5.7789e-05 2e-04 0.9877
## model AIC
## 1 2 14483.87
## 2 2a 14485.87
## 3 2b 14469.11
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.34766 0.25540 1.361 0.174
## alpha 0.70227 0.09501 7.391 2.51e-13 ***
## A 142.90894 13.48623 10.597 < 2e-16 ***
## k 39.02880 3.98802 9.787 < 2e-16 ***
## s 1.74387 0.18179 9.593 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.49 on 1385 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 6.83e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1385 337.23
## 2 1384 325.82 1 11.409 48.464 5.181e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 14469.11
## 2 4 14488.37
## 3 5 14442.53##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.34162 0.25201 1.356 0.175
## alpha 0.70124 0.09431 7.435 1.82e-13 ***
## a 24.39435 4.05270 6.019 2.24e-09 ***
## b 93.28179 7.41989 12.572 < 2e-16 ***
## c 102.73710 8.92197 11.515 < 2e-16 ***
## d 1.13595 0.10865 10.455 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4852 on 1384 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 439 237.09
## 2 438 235.09 1 2.0089 3.7429 0.05368 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4609.958
## 2 2 4608.197##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.1340 0.6019 -0.223 0.82393
## alpha 0.3504 0.1744 2.009 0.04512 *
## A 320.3752 106.7015 3.003 0.00283 **
## k 143.2259 52.7209 2.717 0.00686 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7326 on 438 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 5.634e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 438 235.09
## 2 437 234.74 1 0.3499 0.6514 0.4201
## model AIC
## 1 2 4608.197
## 2 2a 4609.539
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.1340 0.6019 -0.223 0.82393
## alpha 0.3504 0.1744 2.009 0.04512 *
## A 320.3752 106.7015 3.003 0.00283 **
## k 143.2259 52.7209 2.717 0.00686 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7326 on 438 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 5.634e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 437 226.64
## 2 436 221.69 1 4.9467 9.7286 0.001934 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 4608.197
## 2 4 4594.028
## 3 5 4586.274##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.2440 0.5501 -0.443 0.657650
## alpha 0.5283 0.1577 3.350 0.000877 ***
## a 9.5645 1.9483 4.909 1.30e-06 ***
## b 88.5138 12.4743 7.096 5.24e-12 ***
## c 55.9913 5.9220 9.455 < 2e-16 ***
## d 1.0392 0.1138 9.129 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7131 on 436 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (only 64 observations)
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"262 - California Dry Steppe
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (0 observations)
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"313 - Colorado Plateau Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"322 - American Semidesert and Desert
model selection 1
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed## model AIC
## 1 1 NA
## 2 2 NA## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) :
## object 'nls_322.' not foundsummary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"- Cannot fit model
- not enough data (only 3 observations)
331 - Great Plains/Palouse Dry Steppe
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"- Cannot fit model
332 - Great Plains Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 149 87.775
## 2 148 83.201 1 4.5741 8.1365 0.00496 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 1640.707
## 2 2 1634.572##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 3.0055 4.1286 0.728 0.46779
## alpha 0.9714 0.2977 3.263 0.00137 **
## A 231.9254 226.9888 1.022 0.30857
## k 219.8242 199.9830 1.099 0.27346
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7498 on 148 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.357e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 148 83.201
## 2 147 83.108 1 0.093179 0.1648 0.6854
## model AIC
## 1 2 1634.572
## 2 2a NA
## 3 2b 1636.402
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 3.0055 4.1286 0.728 0.46779
## alpha 0.9714 0.2977 3.263 0.00137 **
## A 231.9254 226.9888 1.022 0.30857
## k 219.8242 199.9830 1.099 0.27346
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7498 on 148 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.357e-06
## (2 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: fits
- add s+p model: does not fit
model selection 3
## Error in nls(f_5, data = G_332, start = c(tau = tau.start, alpha = alpha.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 2 1634.572
## 2 4 1636.879
## 3 5 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 3.0055 4.1286 0.728 0.46779
## alpha 0.9714 0.2977 3.263 0.00137 **
## A 231.9254 226.9888 1.022 0.30857
## k 219.8242 199.9830 1.099 0.27346
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7498 on 148 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.357e-06
## (2 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: does not fit
predict and plot
plotting 2
341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
simple log-normal model: does not fit
log-normal phi model: does not fit
model not fitted because only 62 observations
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"342 - Intermountain Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"411 - Everglades
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5103 963.25
## 2 5102 841.07 1 122.19 741.21 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 54262.24
## 2 2 53571.63##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.63454 0.16362 3.878 0.000107 ***
## alpha 0.80068 0.02686 29.811 < 2e-16 ***
## A 446.29921 29.09383 15.340 < 2e-16 ***
## k 198.11601 13.75314 14.405 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.406 on 5102 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.889e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5102 841.07
## 2 5101 833.07 1 8.0008 48.99 2.905e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 53571.63
## 2 2a 53524.82
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.51537 0.15576 3.309 0.000944 ***
## alpha 0.81328 0.02703 30.083 < 2e-16 ***
## A 324.77328 20.26162 16.029 < 2e-16 ***
## k 102.66625 10.74934 9.551 < 2e-16 ***
## p -0.05130 0.01127 -4.551 5.47e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4041 on 5101 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.641e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5101 952.58
## 2 5100 828.03 1 124.55 767.12 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 53524.82
## 2 4 54209.36
## 3 5 53495.89##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.53028 0.15658 3.387 0.000713 ***
## alpha 0.81390 0.02671 30.470 < 2e-16 ***
## a 14.56503 2.98921 4.873 1.14e-06 ***
## b 155.65092 10.10200 15.408 < 2e-16 ***
## c 179.79825 19.79447 9.083 < 2e-16 ***
## d 1.58647 0.10396 15.261 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4029 on 5100 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5180 879.40
## 2 5179 824.61 1 54.79 344.11 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 57351.18
## 2 2 57019.77##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.69968 0.13285 5.267 1.45e-07 ***
## alpha 0.82371 0.04201 19.609 < 2e-16 ***
## A 266.46784 10.04611 26.524 < 2e-16 ***
## k 61.97132 3.14535 19.703 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.399 on 5179 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.081e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5179 824.61
## 2 5178 823.80 1 0.8171 5.1361 0.02347 *
## 3 5178 817.30 0 0.0000
## 4 5177 805.02 1 12.2794 78.9674 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 57019.77
## 2 2a 57016.63
## 3 2b 56975.59
## 4 2c 56899.12##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.87739 0.14139 6.206 5.87e-10 ***
## alpha 0.82469 0.03959 20.832 < 2e-16 ***
## A 162.45200 5.61416 28.936 < 2e-16 ***
## k 37.03352 1.05271 35.179 < 2e-16 ***
## p 0.20173 0.01784 11.310 < 2e-16 ***
## s 2.64792 0.19044 13.904 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3943 on 5177 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.479e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5178 862.65
## 2 5177 803.67 1 58.977 379.91 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 56899.12
## 2 4 57255.49
## 3 5 56890.45##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.87572 0.14097 6.212 5.64e-10 ***
## alpha 0.82430 0.03969 20.766 < 2e-16 ***
## a 31.76130 2.62008 12.122 < 2e-16 ***
## b 122.35089 4.61204 26.529 < 2e-16 ***
## c 103.12833 4.07801 25.289 < 2e-16 ***
## d 1.27367 0.05860 21.735 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.394 on 5177 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 596 80.866
## 2 595 71.900 1 8.9663 74.2 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6115.535
## 2 2 6047.140##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.07855 0.26298 -0.299 0.765
## alpha 0.89957 0.09748 9.228 < 2e-16 ***
## A 298.68647 41.73938 7.156 2.45e-12 ***
## k 95.82372 18.87728 5.076 5.16e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3476 on 595 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 5.77e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 595 71.900
## 2 594 71.708 1 0.19119 1.5837 0.2087
## model AIC
## 1 2 6047.140
## 2 2a 6047.545
## 3 2b 6048.497
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.07855 0.26298 -0.299 0.765
## alpha 0.89957 0.09748 9.228 < 2e-16 ***
## A 298.68647 41.73938 7.156 2.45e-12 ***
## k 95.82372 18.87728 5.076 5.16e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3476 on 595 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 5.77e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 594 80.723
## 2 593 71.768 1 8.9544 73.988 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 6047.140
## 2 4 6118.473
## 3 5 6050.044##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.07855 0.26298 -0.299 0.765
## alpha 0.89957 0.09748 9.228 < 2e-16 ***
## A 298.68647 41.73938 7.156 2.45e-12 ***
## k 95.82372 18.87728 5.076 5.16e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3476 on 595 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 5.77e-06
## (3 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 676 152.77
## 2 675 142.27 1 10.498 49.809 4.216e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7025.553
## 2 2 6979.211##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.5697 0.5042 1.130 0.259
## alpha 0.8583 0.1139 7.536 1.57e-13 ***
## A 315.8268 62.8438 5.026 6.44e-07 ***
## k 147.8427 33.1149 4.465 9.40e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4591 on 675 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.062e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 675 142.27
## 2 674 142.26 1 0.0098593 0.0467 0.8290
## 3 674 142.26 0 0.0000000
## 4 673 142.26 1 0.0069224 0.0327 0.8564
## model AIC
## 1 2 6979.211
## 2 2a 6981.164
## 3 2b 6981.181
## 4 2c 6983.148##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.5697 0.5042 1.130 0.259
## alpha 0.8583 0.1139 7.536 1.57e-13 ***
## A 315.8268 62.8438 5.026 6.44e-07 ***
## k 147.8427 33.1149 4.465 9.40e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4591 on 675 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.062e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Error in nls(f_5, data = G_M231, start = c(tau = tau.start, alpha = alpha.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 2 6979.211
## 2 4 7029.273
## 3 5 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.5697 0.5042 1.130 0.259
## alpha 0.8583 0.1139 7.536 1.57e-13 ***
## A 315.8268 62.8438 5.026 6.44e-07 ***
## k 147.8427 33.1149 4.465 9.40e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4591 on 675 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.062e-06
## (1 observation deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: does not fit
predict and plot
plotting 2
M242 - Cascade Mixed Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 326 100.337
## 2 325 98.647 1 1.6905 5.5696 0.01887 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3504.259
## 2 2 3500.669##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.5690 1.1894 1.319 0.18805
## alpha 0.6751 0.2661 2.537 0.01165 *
## A 85.0151 18.2427 4.660 4.61e-06 ***
## k 22.9171 7.8626 2.915 0.00381 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5509 on 325 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 7.882e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 325 98.647
## 2 324 97.539 1 1.10741 3.6785 0.0560 .
## 3 324 93.712 0 0.00000
## 4 323 93.308 1 0.40411 1.3989 0.2378
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 3500.669
## 2 2a 3498.954
## 3 2b 3485.785
## 4 2c 3486.363##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.8945 1.2923 1.466 0.1436
## alpha 0.6580 0.2763 2.381 0.0178 *
## A 65.9248 13.3842 4.926 1.34e-06 ***
## k 30.8188 3.7464 8.226 4.75e-15 ***
## s 42.5340 187.7406 0.227 0.8209
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5378 on 324 degrees of freedom
##
## Number of iterations to convergence: 21
## Achieved convergence tolerance: 8.771e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 324 96.856
## 2 323 95.476 1 1.38 4.6688 0.03145 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 3485.785
## 2 4 3496.641
## 3 5 3493.920##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.8945 1.2923 1.466 0.1436
## alpha 0.6580 0.2763 2.381 0.0178 *
## A 65.9248 13.3842 4.926 1.34e-06 ***
## k 30.8188 3.7464 8.226 4.75e-15 ***
## s 42.5340 187.7406 0.227 0.8209
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5378 on 324 degrees of freedom
##
## Number of iterations to convergence: 21
## Achieved convergence tolerance: 8.771e-06
## (1 observation deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
M262 - California coastal range - coniferous forest - open woodland - shrub meadow
Model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
simple log-normal model: does not fit
log-normal phi model: does not fit
model can fit - but K is negative (only 19 observations) - model excluded
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 299 124.35
## 2 298 113.37 1 10.974 28.846 1.581e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3013.807
## 2 2 2987.903##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.07662 0.66159 0.116 0.90788
## alpha 0.77829 0.12977 5.998 5.79e-09 ***
## A 99.54181 19.23214 5.176 4.18e-07 ***
## k 53.05797 17.65911 3.005 0.00289 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6168 on 298 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.942e-06
## (4 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 298 113.37
## 2 297 113.26 1 0.115630 0.3032 0.5823
## 3 297 113.00 0 0.000000
## 4 296 112.91 1 0.094618 0.2480 0.6188
## model AIC
## 1 2 2987.903
## 2 2a 2989.595
## 3 2b 2988.916
## 4 2c 2990.663## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df_bal$Ecoprovince == "M334", :
## provided 33 variables to replace 32 variables##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.07662 0.66159 0.116 0.90788
## alpha 0.77829 0.12977 5.998 5.79e-09 ***
## A 99.54181 19.23214 5.176 4.18e-07 ***
## k 53.05797 17.65911 3.005 0.00289 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6168 on 298 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.942e-06
## (4 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 297 124.07
## 2 296 113.29 1 10.775 28.151 2.203e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 2987.903
## 2 4 3017.126
## 3 5 2991.690##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.07662 0.66159 0.116 0.90788
## alpha 0.77829 0.12977 5.998 5.79e-09 ***
## A 99.54181 19.23214 5.176 4.18e-07 ***
## k 53.05797 17.65911 3.005 0.00289 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6168 on 298 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.942e-06
## (4 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
predict and plot
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Ecoprovince | Ecoregion | Sel.Mod.2 | Sel.Mod.3 | Best.Mod |
|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | 2 | 5 | 5 |
| 212 | Laurentian Mixed Forest | 2a | 5 | 5 |
| 221 | Eastern Broadleaf Forest | 2b | 5 | 5 |
| 222 | Midwest Broadleaf Forest | 2a | 5 | 5 |
| 223 | Central Interior Broadleaf Forest | 2c | 5 | 5 |
| 231 | Southeastern Mixed Forest | 2c | 5 | 5 |
| 232 | Outer Coastal Plain Mixed Forest | 2a | 5 | 5 |
| 234 | Lower Mississippi Riverine Forest | 2c | 5 | 5 |
| 242 | Pacific Lowland Mixed Forest | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | 2b | 5 | 5 |
| 255 | Prairie Parkland (Subtropical) | 2 | 5 | 5 |
| 261 | California Coastal Chaparral Forest and Shrub | NA | NA | NA |
| 262 | California Dry Steppe | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | NA | NA | NA |
| 322 | American Semidesert and Desert | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA | NA | NA |
| 332 | Great Plains Steppe | 2 | 2 | 2 |
| 341 | Intermountain Semi-Desert and Desert | NA | NA | NA |
| 342 | Intermountain Semi-Desert | NA | NA | NA |
| 411 | Everglades | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2a | 5 | 5 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 2c | 5 | 5 |
| M223 | Ozark Broadleaf Forest Meadow | 2 | 2 | 2 |
| M231 | Ouachita Mixed Forest | 2 | 2 | 2 |
| M242 | Cascade Mixed Forest | NA | NA | NA |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 2b | 2b | 2b |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M334 | Black Hills Coniferous Forest | 2 | 2 | 2 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA | NA | NA |
table by ecoprovince
| Ecoprovince | Ecoregion | region | n.obs | n.plots | tau | tau.variance | tau.2.5 | tau.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 | a | a.2.5 | a.97.5 | b | b.se | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 4838 | 2419 | 0.5811807 | 0.0315130 | 0.2331627 | 0.9291986 | 0.8407842 | 0.0011638 | 0.7739056 | 0.9076629 | 473.76484 | 401.22103 | 546.30865 | 205.69316 | 169.97959 | 241.40674 | 33.400705 | 29.493797 | 37.30761 | 118.88478 | NA | 107.26593 | 130.50363 | 118.37512 | 106.88772 | 129.86252 | 1.016528 | 0.9139327 | 1.119122 |
| 212 | Laurentian Mixed Forest | east | 12962 | 6481 | 1.1905141 | 0.0185145 | 0.9238008 | 1.4572274 | 0.6733287 | 0.0007299 | 0.6203705 | 0.7262870 | 192.14309 | 173.82377 | 210.46242 | 108.46141 | 92.82129 | 124.10153 | 13.385905 | 12.379552 | 14.39226 | 75.80154 | NA | 71.16321 | 80.43987 | 121.05709 | 110.36363 | 131.75055 | 1.415947 | 1.3319180 | 1.499977 |
| 221 | Eastern Broadleaf Forest | east | 5446 | 2723 | 0.2422230 | 0.0169479 | -0.0129899 | 0.4974359 | 0.8082238 | 0.0009532 | 0.7476984 | 0.8687492 | 293.53650 | 251.49470 | 335.57830 | 64.20469 | 51.62403 | 76.78536 | 21.082556 | 15.831554 | 26.33356 | 179.51639 | NA | 159.02822 | 200.00457 | 156.83930 | 126.03502 | 187.64358 | 1.518786 | 1.3427586 | 1.694814 |
| 222 | Midwest Broadleaf Forest | east | 3552 | 1776 | 1.2114537 | 0.0651252 | 0.7111070 | 1.7118003 | 0.7688102 | 0.0029588 | 0.6621620 | 0.8754583 | 342.27169 | 256.80774 | 427.73563 | 170.04542 | 113.41537 | 226.67548 | 14.018976 | 11.290384 | 16.74757 | 101.92211 | NA | 90.10999 | 113.73424 | 115.56990 | 99.46147 | 131.67834 | 1.197007 | 1.0662985 | 1.327715 |
| 223 | Central Interior Broadleaf Forest | east | 6388 | 3194 | 0.8461273 | 0.0146625 | 0.6087525 | 1.0835021 | 0.7112156 | 0.0011445 | 0.6448959 | 0.7775352 | 127.11413 | 118.06312 | 136.16514 | 37.02397 | 34.56160 | 39.48633 | 17.800944 | 13.742432 | 21.85946 | 98.51432 | NA | 90.85761 | 106.17104 | 113.18502 | 99.49412 | 126.87591 | 1.445696 | 1.2995960 | 1.591796 |
| 231 | Southeastern Mixed Forest | east | 7790 | 3895 | 1.4759858 | 0.0331065 | 1.1193112 | 1.8326605 | 0.6508476 | 0.0005086 | 0.6066399 | 0.6950552 | 144.97930 | 132.73182 | 157.22678 | 30.16077 | 27.76581 | 32.55574 | 16.127853 | 14.505323 | 17.75038 | 120.36292 | NA | 109.42373 | 131.30210 | 112.83900 | 94.67141 | 131.00659 | 1.633502 | 1.5036347 | 1.763370 |
| 232 | Outer Coastal Plain Mixed Forest | east | 7940 | 3970 | 1.0085159 | 0.0364082 | 0.6344793 | 1.3825526 | 0.7104306 | 0.0004570 | 0.6685254 | 0.7523358 | 408.34768 | 328.15225 | 488.54310 | 159.56714 | 117.80214 | 201.33213 | 20.518658 | 18.511922 | 22.52539 | 121.27486 | NA | 108.92335 | 133.62637 | 111.11452 | 92.96303 | 129.26601 | 1.502835 | 1.3689187 | 1.636751 |
| 234 | Lower Mississippi Riverine Forest | east | 830 | 415 | 0.4023597 | 0.1697654 | -0.4063858 | 1.2111052 | 0.7883253 | 0.0049140 | 0.6507290 | 0.9259216 | 395.47217 | 23.90610 | 767.03825 | 99.96670 | -38.80593 | 238.73932 | 0.000000 | -11.644423 | 11.64442 | 340.82383 | NA | -60.32947 | 741.97714 | 675.40707 | -1170.66705 | 2521.48119 | 2.554711 | 1.2035154 | 3.905907 |
| 242 | Pacific Lowland Mixed Forest | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 1392 | 696 | 0.3416233 | 0.0635084 | -0.1527370 | 0.8359836 | 0.7012428 | 0.0088949 | 0.5162318 | 0.8862538 | 142.90894 | 116.45330 | 169.36458 | 39.02880 | 31.20558 | 46.85201 | 24.394348 | 16.444251 | 32.34445 | 93.28179 | NA | 78.72633 | 107.83724 | 102.73710 | 85.23504 | 120.23915 | 1.135955 | 0.9228090 | 1.349101 |
| 255 | Prairie Parkland (Subtropical) | east | 444 | 222 | -0.2439613 | 0.3026388 | -1.3251902 | 0.8372676 | 0.5283394 | 0.0248661 | 0.2184128 | 0.8382661 | 320.37518 | 110.66455 | 530.08580 | 143.22594 | 39.60855 | 246.84333 | 9.564518 | 5.735244 | 13.39379 | 88.51384 | NA | 63.99654 | 113.03113 | 55.99135 | 44.35208 | 67.63061 | 1.039193 | 0.8154724 | 1.262914 |
| 261 | California Coastal Chaparral Forest and Shrub | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | west | 4 | 2 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | west | 118 | 59 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | west | 154 | 77 | 3.0054586 | 17.0455900 | -5.1532211 | 11.1641382 | 0.9713883 | 0.0886175 | 0.3831227 | 1.5596540 | 231.92537 | -216.63238 | 680.48311 | 219.82421 | -175.36661 | 615.01504 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 341 | Intermountain Semi-Desert and Desert | west | 4 | 2 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | west | 2 | 1 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 66 | 33 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 5108 | 2554 | 0.5302798 | 0.0245169 | 0.2233184 | 0.8372412 | 0.8138994 | 0.0007135 | 0.7615330 | 0.8662658 | 324.77328 | 285.05180 | 364.49475 | 102.66625 | 81.59293 | 123.73957 | 14.565033 | 8.704894 | 20.42517 | 155.65092 | NA | 135.84666 | 175.45518 | 179.79825 | 140.99259 | 218.60392 | 1.586471 | 1.3826673 | 1.790274 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 5186 | 2593 | 0.8757158 | 0.0198734 | 0.5993491 | 1.1520824 | 0.8243016 | 0.0015756 | 0.7464844 | 0.9021187 | 162.45200 | 151.44589 | 173.45812 | 37.03352 | 34.96976 | 39.09727 | 31.761299 | 26.624837 | 36.89776 | 122.35089 | NA | 113.30935 | 131.39243 | 103.12833 | 95.13370 | 111.12296 | 1.273667 | 1.1587869 | 1.388547 |
| M223 | Ozark Broadleaf Forest Meadow | east | 602 | 301 | -0.0785477 | 0.0691598 | -0.5950347 | 0.4379392 | 0.8995732 | 0.0095032 | 0.7081176 | 1.0910287 | 298.68647 | 216.71203 | 380.66091 | 95.82372 | 58.74951 | 132.89792 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M231 | Ouachita Mixed Forest | east | 680 | 340 | 0.5697483 | 0.2542625 | -0.4203280 | 1.5598245 | 0.8582543 | 0.0129720 | 0.6346241 | 1.0818845 | 315.82677 | 192.43391 | 439.21963 | 147.84274 | 82.82219 | 212.86329 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M242 | Cascade Mixed Forest | west | 34 | 17 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | west | 330 | 165 | 1.8945480 | 1.6701111 | -0.6478649 | 4.4369609 | 0.6580466 | 0.0763610 | 0.1144095 | 1.2016837 | 65.92482 | 39.59387 | 92.25577 | 30.81882 | 23.44844 | 38.18920 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | west | 8 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | west | 20 | 10 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | west | 22 | 11 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M334 | Black Hills Coniferous Forest | west | 306 | 153 | 0.0766154 | 0.4376976 | -1.2253593 | 1.3785901 | 0.7782879 | 0.0168399 | 0.5229091 | 1.0336667 | 99.54181 | 61.69380 | 137.38982 | 53.05797 | 18.30561 | 87.81033 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
parameter variance co-variance
plot tau
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
plot alpha (biomass compensation effect)
plot A (asymptote of B)
## Warning: Removed 19 rows containing missing values (`geom_point()`).
plot k (stand age at half biomass asymptote)
## Warning: Removed 19 rows containing missing values (`geom_point()`).
Model Bookeeping
The model bookeeping code begins here. See the methods of the main paper for specific details, but briefly, biomass change attribution to a given driver. either: 1. changes in stand age, 2: productivity trends (as a function of measurement year), or 3: disturbance (quantified as the change in the plot fractional Biomass loss) are calculated by taking the difference between the last and first FIA plot re-measurement in the temporally-balanced dataset. For the Biomass Change (DeltaB) component in question, we use predict on the nls model varying only the given driver between the last and first re-measurement and setting the other drivers to value at the first re-measurement.
For errors in the various biomass change components, we account for model parameter uncertainty. We simulate 9999 parameter draws from the multivariate normal distribution of the nls model parameter space and predict the age function (f(x)) only using model estimates of alpha and tau in the same manner as described above.
Additional code for bookeeping model validation and plots for the supplemental information of the manuscript is contained below.
1. Set up Dataframes & Calculate Empirical Delta-B total
2. Delta-B due to Delta-STDAGE
simulate f(age) - Variance in DeltaB_age – rmvnorm
3. Delta-B due to productivity trend
simulate f(year) - Variance in DeltaB_productivity trend – rmvnorm
4. Delta-B due to disturbance
simulate f(disturbance) - Variance in DeltaB_disturbance – rmvnorm
plotting loss rate - first & last
BK_df (Bookeeping Dataframe)
BK_df avgs (Bookeeping averages by Ecoprovince)
Comparing & Checking Delta_B Model Bookeeping
compare DeltaB_oberved and DeltaB_SUM_total
## `geom_smooth()` using formula = 'y ~ x'
Delta B age vs. Delta Stand age
## `geom_smooth()` using formula = 'y ~ x'
Delta B_productivity trend vs. tau
## `geom_smooth()` using formula = 'y ~ x'
Delta B_disturbance vs. -alpha X MBL
## `geom_smooth()` using formula = 'y ~ x'
plotting Delta B
bookeping fig take 1
bookeeping fig - take 2
## Warning: Removed 15738 rows containing missing values (`geom_point()`).
### 6. stand age densities
make a fig
## Warning: package 'ggridges' was built under R version 4.2.2## Picking joint bandwidth of 4.73## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).## Warning: Using the `size` aesthietic with geom_segment was deprecated in ggplot2 3.4.0.
## ℹ Please use the `linewidth` aesthetic instead.
Fig. 3 – combined bookeeper with stand age densities
## Picking joint bandwidth of 4.73## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).
relationship of DeltaB_observed and DeltaB_productivity trend
##
## Pearson's product-moment correlation
##
## data: BK_df$DeltaB_year and BK_df$DeltaB_total
## t = -16.291, df = 31577, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.10222372 -0.08034876
## sample estimates:
## cor
## -0.09129725##
## Pearson's product-moment correlation
##
## data: year_avg_merger1$value_year and year_avg_merger1$value_total
## t = 2.6013, df = 12, p-value = 0.02317
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1025738 0.8577687
## sample estimates:
## cor
## 0.6004734## `geom_smooth()` using formula = 'y ~ x'
relationship of DeltaB_observed and DeltaB_age
##
## Pearson's product-moment correlation
##
## data: BK_df$DeltaB_age and BK_df$DeltaB_total
## t = 116.95, df = 31577, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.5420054 0.5573981
## sample estimates:
## cor
## 0.5497484##
## Pearson's product-moment correlation
##
## data: year_avg_merger2$value_age and year_avg_merger2$value_total
## t = 2.1683, df = 12, p-value = 0.05095
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -1.667272e-05 8.280454e-01
## sample estimates:
## cor
## 0.5305675## `geom_smooth()` using formula = 'y ~ x'
relationship of DeltaB_observed and DeltaB_disturbance
##
## Pearson's product-moment correlation
##
## data: BK_df$DeltaB_disturbance and BK_df$DeltaB_total
## t = 138.31, df = 31577, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.6072941 0.6210318
## sample estimates:
## cor
## 0.6142095##
## Pearson's product-moment correlation
##
## data: year_avg_merger3$value_disturbance and year_avg_merger3$value_total
## t = -0.4265, df = 12, p-value = 0.6773
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.6130306 0.4366957
## sample estimates:
## cor
## -0.1221971## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
plotting compare Delta B altogether
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'## Warning: ggrepel: 8 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps## Warning: ggrepel: 5 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps## Warning: ggrepel: 3 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps